TY - JOUR AU1 - Pham, Thang AU2 - Vinh, Le AU3 - de Zeeuw, Frank AB - We determine which quadratic polynomials in three variables are expanders over an arbitrary field $$\mathbb{F}$$ F . More precisely, we prove that for a quadratic polynomial f ∈ $$\mathbb{F}$$ F [x,y,z], which is not of the form g(h(x)+k(y)+l(z)), we have |f(A×B×C)|≫N 3/2 for any sets A,B,C ⊂ $$\mathbb{F}$$ F with |A|=|B|=|C|=N, with N not too large compared to the characteristic of F. TI - Three-Variable Expanding Polynomials and Higher-Dimensional Distinct Distances JF - Combinatorica DO - 10.1007/s00493-017-3773-y DA - 2018-06-05 UR - https://www.deepdyve.com/lp/springer-journals/three-variable-expanding-polynomials-and-higher-dimensional-distinct-DuhfY84WEZ SP - 411 EP - 426 VL - 39 IS - 2 DP - DeepDyve ER -